Alvarez (elbow) threw a 26-pitch bullpen session Sunday, T.R. Sullivan of MLB.com reports.
Alvarez last appeared in a game May 26 before being diagnosed with the strained left elbow, so he would be eligible to come off the disabled list as soon as the Rangers deem him ready to go. The team is expected to decide later this week whether Alvarez will be activated or head out on a minor-league rehab assignment.